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2003 Austria Beginners' Competition
1
1
Part of
2003 Austria Beginners' Competition
Problems
(1)
max [\sqrt{[\sqrt{x+y}]}] if [\sqrt{x}] = 10 and [\sqrt{x}] =14
Source: 2003 Austria Beginners' Competition p1
10/4/2022
For the real numbers
x
x
x
and
y
y
y
,
[
x
]
=
10
[\sqrt{x}] = 10
[
x
]
=
10
and
[
y
]
=
14
[\sqrt{y}] =14
[
y
]
=
14
. How large is
[
[
x
+
y
]
]
\left[\sqrt{[ \sqrt{x+y} ]}\right]
[
[
x
+
y
]
]
?(Note: the square roots are the positive values and
[
x
]
[x]
[
x
]
is the largest integer less than or equal to x.)
algebra
floor function